Question

to find the equation of a regression line, $hat{y}=ax + b$, you need these formulas: $a = r\frac{s_y}{s_x}$, $b=\bar{y}-a\bar{x}$. a regression line has a slope of 1.885. if the mean of the x - coordinates of the data points is 3.448, and the mean of the y - coordinates is 12.318, what is the y - value of the y - intercept of the line to three decimal places? a. -5.819 b. 19.771

Explanation:

Step1: Identify the given values

We know that $a = 1.885$, $\bar{x}=3.448$, $\bar{y}=12.318$. The formula for the $y$-intercept $b$ of the regression - line is $b=\bar{y}-a\bar{x}$.

Step2: Substitute the values into the formula

$b = 12.318-1.885\times3.448$.
First, calculate $1.885\times3.448$: $1.885\times3.448 = 1.885\times(3 + 0.4+0.04 + 0.008)=1.885\times3+1.885\times0.4+1.885\times0.04+1.885\times0.008=5.655+0.754+0.0754 + 0.01508=6.49948$.
Then, calculate $b$: $b = 12.318-6.49948 = 5.81852\approx5.819$.

Answer:

A. - 5.819